Finite difference schemes for the parabolic p-Laplace equation

  1. Félix del Teso 1
  2. Erik Lindgren 2
  1. 1 Departamento de Matematicas, Universidad Autónoma de Madrid (UAM)
  2. 2 Department of Mathematics, KTH-Royal Institute of Technology, Stockholm
Journal:
SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada

ISSN: 2281-7875

Year of publication: 2023

Volume: 80

Issue: 4

Pages: 527-547

Type: Article

DOI: 10.1007/S40324-022-00316-Y DIALNET GOOGLE SCHOLAR

More publications in: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada

Abstract

We propose a new finite difference scheme for the degenerate parabolic equation ∂tu − div(|∇u|p−2∇u) = f , p ≥ 2. Under the assumption that the data is Hölder continuous, we establish the convergence of the explicit-in-time scheme for the Cauchy problem provided a suitable stability type CFLcondition. An important advantage of our approach, is that the CFL-condition makes use of the regularity provided by the scheme to reduce the computational cost. In particular, for Lipschitz data, the CFL-condition is of the same order as for the heat equation and independent of p.

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